"All of the sudden, we're cast into a situation here which is 'sit down and shut up, we got the votes, tough,' " he said. "That's our frustration."

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"I know there are new members that just have not experienced what it's like to be said, 'sit down and shut up. We'll tell you what you can say, what amendment you can offer, if any.' "

Coats did not personally criticize Senate Majority Leader Harry Reid (D-Nev.) for invoking the "nuclear option" on nominees, or for limiting debate. But Coats did praise past Democratic leaders.

"This never would have happened if Robert Byrd (D-W.Va.) was here," he said. Other Republicans made the same point in late Thursday night debate.

Coats praised his former majority leader from more than two decades ago. "I respected Majority Leader George Mitchell [(D-Maine)]," he said. "Tough, ran this place like clockwork."

Coats said that since he left the Senate in 2001, the Senate has changed dramatically.

"I don't recognize this Senate today," he said. "I don't recognize this. This is not the Senate that I joined in 1989."

He also warned that Democrats would regret their decision to limit minority rights, possibly as early as the next Congress.

"Democrats are going to rue the day when they made this move and jammed it down our throats and said, 'you don't like it, tough,' " Coats said. "Because at some point the pendulum will swing, and I think maybe sooner than a lot of people think."

Coats predicted that 2014 might be a "turnaround year" for Republicans in the Senate.

"And if it is, [Democrats are] suddenly going to find themselves in the minority," he said. "And we'll see, and they will learn, what it's like to be denied an opportunity to be elected to the United States Senate and be a member of this august body, be one of 100 people that are chosen to represent their states ... and be shut down from having any opportunity whatsoever to have a voice in what goes forward here."

Reid has come under criticism from several House Republicans for limiting consideration of amendments to the National Defense Authorization Act (NDAA) over the last few weeks.

Ultimately, the House had to repass a new NDAA to get around the logjam in the Senate, and the Senate is expected to quickly pass it next week. Limits on NDAA amendments prompted several Republicans to blast Reid for limiting GOP input on national defense policy.